Absorption spectrometry is arguably the most commonly used quantitation technique used for analysis. To increase detection sensitivity, one chooses the optimum chemistry and the measurement wavelength (absorptivity c at maximum). Absorbance also increases with the pathlength. In the gas phase, single long paths as in differential optical absorption spectroscopy or one attained through multi-reflection cells can be used. Simply increasing the absolute value of the absorbance is not tantamount to improving the limit of detection (LOD), however. In the liquid phase, due to increased beam divergence, light is rapidly lost to the wall and the relative noise increases concomitantly as the detector becomes light starved. Thin walled straight glass tubes or those filled with high refractive index (RI) organic solvents help guide light via total internal reflections at the glass-air and solvent-glass interfaces, respectively; neither system is particularly useful: in one case deposition of any particles on the glass outer surface causes loss of light, in the other case, water is the solvent of interest in majority of applications. A gas shell can be formed around a liquid in a hydrophobic porous membrane tube but a gas bubble is too readily formed. Aqueous solutions containing a lot of solute or ethanol can have an RI greater than that of FEP Teflon®1.34 and thus a FEP tube filled with such a solution also behaves as a liquid core waveguide (LCW). LCWs with a purely aqueous solution as the core have become practical only after the introduction of Teflon AF (RI 1.29-1.31, compared to 1.33 for water).
In all the above arrangements, the incident light assumedly traces a single path; these are both single path and single-pass cells, i.e., the light does not trace the same path twice. Such cells have a single effective overall pathlength for the purposes of Lambert-Beer's law regardless of the cell contents. If a particular chemistry—wavelength combination leads to a certain dynamic range, changing the pathlength can merely change the location of the usable range in the concentration domain.
In contrast, a multipath arrangement behaves differently. If the shortest path that the light can travel to reach the detector is b, the effective pathlength (henceforth designated b) is absorbance dependent. It can be perceived that at high absorbances, longer paths contributes little to the transmitted light and
            lim              A        =        ∞              ⁢          b      _        =      b    .  The value or b at the lower absorbance limit is of greater interest as it is often the determinant of the concentration limit of detection (LOD). For a multiplicity of pathlengths bi, each having fi fraction of the total light (Σfi=1), it has been shown that b at the lower absorbance limit is simply the weighted sum b=Σfibi. For an evenly illuminated wedge shaped cell, for example, at the lower absorbance limit b can be half the base width of the cell.
The combination of cells with different pathlengths, as in a wedge-shaped cell, is not practical; moreover,
      lim          A      =      0        ⁢      b    _  can still be less than the longest physical pathlength. Putting partially reflective mirrors on both the entrance and exit windows of any conventional cell can serve the same purpose. Such a system, hereinafter called a single-path multipass cell (multiple reflections on the same path as the beam traverses back and forth, each time losing light both due to absorption by the medium and transmission through the partially transmissive mirrors), is provided in order to increase the pathlength, especially at the low absorbance end.
It can be shown that the gain in pathlength at the low absorbance limit is equal to
            1      +              R        2                    1      -              R        2              ,where R is the reflectivity of the mirror (R being 1 for a perfectly reflective mirror and 0 for a perfectly transparent object). It can be further shown that for values of R approaching 1,
      1    +          R      2            1    -          R      2      is well approximated by
      1          1      -      R        .Thus for example, a cell with a physical pathlength of 1 cm, bounded by mirrors of 99% reflectivity (R=0.99) will have an effective path length of
      b    _    =            1              1        -        R              =          100      ⁢                          ⁢              cm        .            
While an increase in the mirror reflectivity R increases the pathlength and a proportionate amplification of absorbance, increases in R also results in lower light throughput and increases the relative noise of the detector. With R=0.99 mirrors for example, with 10,000 photons incident on the entrance mirror, only 100 photons will make into the cell and if there is no attenuation by the solution in the cell, of 100 photons making it to the exit mirror only 1 will exit to reach the detector. What is needed then is a means for increasing light throughput without significant loss of cavity enhancement and reducing the need for increased source brightness for sufficient light to reach the detector.